User:Tohline/Math/EQ EllipticIntegral03
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<math>~K(\mu)</math> |
<math>~=</math> |
<math>~ \ln \frac{4}{k^'} + \frac{1}{2^2}\biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} \biggr)(k')^2 + \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} \biggr)(k')^4 + \biggl( \frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\biggr)^2 \biggl( \ln\frac{4}{k^'} - \frac{2}{1\cdot 2} - \frac{2}{3\cdot 4} - \frac{2}{5\cdot 6} \biggr)(k')^6 ~+~ \cdots </math> |
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Gradshteyn & Ryzhik (1965), §8.113.3 |
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where: <math>~k^' \equiv (1 - \mu^2)^{1 / 2}</math> |
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